相关论文: A search on the Klein-Gordon equation
We consider the semilinear wave equation in higher dimensions with power nonlinearity in the super-conformal range, and its perturbations with lower order terms, including the Klein-Gordon equation. We improve the upper bounds on blow-up…
We consider the coupled systems of nonlinear wave and Klein-Gordon equations in two space dimensions with cubic nonlinearity. For this kind of systems, the small data global existence is already known if the cubic nonlinearity satisfies a…
Witten's non-relativistic formalism of supersymmetric quantum mechanics was based on a factorization and partnership between Schroedinger equations. We show how it accommodates a transition to the partnership between relativistic…
Exact solutions of two-particle relativistic equations of quantum field theory describing the scattering $s$-states and the bound $s$-states are found in the cases of delta-shell potential and superposition of delta-shell potentials. Some…
Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The frequency of perturbation varies slowly and passes through a resonance. The resonance generates a solitary packets of waves. Full…
We analyse the complex-valued Klein-Gordon Equation from an integrability perspective by the implementation of the Lie Theory of Continuous Groups, where this equation is governed by power-law nonlinearity. We write the equations in terms…
In this article we will prove the global existence of a type of wave-Klein-Gordon system in $2+1$ spacetime dimension. Some technical tools such as conformal energy estimate on hyperboloid, normal form transform on Klein-Gordon equations…
The charge spreading of ground and excited states of Klein-Gordon particles moving in a Coulomb potential is quantitatively analyzed by means of the ordinary moments and the Heisenberg measure as well as by use of the most relevant…
The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component…
In this article we used supersymmetry quantum mechanics and factorization methods to study the bound and scattering state of Klein-Gordon equation with deformed Hulthen plus deformed hyperbolical potential for arbitrary state in…
We are interested in the Klein-Gordon-Zakharov system in $\mathbb{R}^{1+2}$, which is an important model in plasma physics with extensive mathematical studies. The system can be regarded as semilinear coupled wave and Klein-Gordon equations…
In this paper, we study the long time behavior of energy solutions for a class of wave equation with time-dependent mass and speed of pro\-pagation. We introduce a classification of the potential term, which clarifies whether the solution…
A numerical approach is proposed for studying the quantum optical modes in the Klein-Gordon lattices where the energy contribution of the atomic displacements is non-quadratic. The features of the biphonon excitations are investigated in…
In this paper we consider a fractional wave equation for hypoelliptic operators with a singular mass term depending on the spacial variable and prove that it has a very weak solution. Such analysis can be conveniently realised in the…
We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy at most slightly above that of the ground…
The quantum hydrodynamic-like equations for two real variables (i.e., the phase and the amplitude of the wave function) of the relativistic Klein-Gordon equation are derived in the present paper. The paper also shows that in classical limit…
We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
The nonlinear Klein-Gordon (NLKG) equation on a manifold $M$ in the nonrelativistic limit, namely as the speed of light $c$ tends to infinity, is considered. In particular, a higher-order normalized approximation of NLKG (which corresponds…
The sine-Gordon model on the half-line with a dynamical boundary introduced by Delius and one of the authors is considered at quantum level. Classical boundary conditions associated with classical integrability are shown to be preserved at…
A multistream model for spinless electrons in a relativistic quantum plasma is introduced by means of a suitable fluid-like version of the Klein-Gordon-Maxwell system. The one and two-stream cases are treated in detail. A new linear…